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A111314
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a(n) = a(n-1) + a(n-2) + 2 where a(0) = a(1) = 1.
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8
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1, 1, 4, 7, 13, 22, 37, 61, 100, 163, 265, 430, 697, 1129, 1828, 2959, 4789, 7750, 12541, 20293, 32836, 53131, 85969, 139102, 225073, 364177, 589252, 953431, 1542685, 2496118, 4038805, 6534925, 10573732, 17108659, 27682393, 44791054, 72473449
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OFFSET
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0,3
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COMMENTS
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This is the sequence A(1,1;1,1;2) of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. - Wolfdieter Lang, Oct 17 2010
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LINKS
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FORMULA
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G.f.: (2x^2-x+1)/((x-1)(x^2+x-1)). - T. D. Noe, Oct 19 2007
a(n) = F(n-1)+F(n+3)-2, where F(n) is the n-th Fibonacci number. - Zerinvary Lajos, Jan 31 2008
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MAPLE
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with(combinat): seq(fibonacci(n-1)+fibonacci(n+3)-2, n=0..35); # Zerinvary Lajos, Jan 31 2008
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MATHEMATICA
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a[0] = a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + 2; Table[ a[n], {n, 0, 36}] (* Robert G. Wilson v *)
RecurrenceTable[{a[0]==a[1]==1, a[n]==a[n-1]+a[n-2]+2}, a, {n, 40}] (* Harvey P. Dale, Mar 27 2022 *)
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PROG
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(Sage) from sage.combinat.sloane_functions import recur_gen2b; it = recur_gen2b(1, 1, 1, 1, lambda n: 2); [next(it) for i in range(1, 38)] # Zerinvary Lajos, Jul 09 2008
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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